Quantum technology has grown out of quantum information theory and now provides a valuable tool that researchers from numerous fields can add to their toolbox of research methods. To date, various systems have been exploited to promote the application of quantum information processing. The systems that can be used for quantum technology include superconducting circuits, ultracold atoms, trapped ions, semiconductor quantum dots, and solid-state spins and emitters. In this review, we will discuss the state-of-the-art of material platforms for spin-based quantum technology, with a focus on the progress in solid-state spins and emitters in several leading host materials, including diamond, silicon carbide, boron nitride, silicon, two-dimensional semiconductors, and other materials. We will highlight how first-principles calculations can serve as an exceptionally robust tool for finding novel defect qubits and single-photon emitters in solids, through detailed predictions of electronic, magnetic, and optical properties.

Material platforms for defect qubits and single-photon emitters

Nanofabricated mechanical resonators are gaining significant momentum among potential quantum technologies due to their unique design freedom and independence from naturally occurring resonances. As their functionality is widely detached from material choice, they constitute ideal tools for transducers—intermediaries between different quantum systems—and as memory elements in conjunction with quantum communication and computing devices. Their capability to host ultra-long-lived phonon modes is particularity attractive for non-classical information storage, both for future quantum technologies and for fundamental tests of physics. Here, we demonstrate a Duan–Lukin–Cirac–Zoller-type mechanical quantum memory with an energy decay time of T1 ≈ 2 ms, which is controlled through an optical interface engineered to natively operate at telecom wavelengths. We further investigate the coherence of the memory, equivalent to the dephasing $${T}_{2}^{* }$$ for qubits, which has a power-dependent value between 15 and 112 μs. This demonstration is enabled by an optical scheme to create a superposition state of $$\left|0\right\rangle +\left|1\right\rangle$$ mechanical excitations, with an arbitrary ratio between the vacuum and single-phonon components. By exploiting the long-lived phonon modes in nanoscale mechanical resonators, a quantum memory that operates around the standard telecom wavelength of 1,550 nm is realized on a silicon platform.

A quantum memory at telecom wavelengths

We propose the dynamical stabilization of a nonequilibrium order in a driven dissipative system comprised an atomic Bose-Einstein condensate inside a high finesse optical cavity, pumped with an optical standing wave operating in the regime of anomalous dispersion. When the amplitude of the pump field is modulated close to twice the characteristic limit-cycle frequency of the unmodulated system, a stable subharmonic response is found. The dynamical phase diagram shows that this subharmonic response occurs in a region expanded with respect to that where stable limit-cycle dynamics occurs for the unmodulated system. In turning on the modulation we tune the atom-cavity system from a continuous to a discrete time crystal.

From a continuous to a discrete time crystal in a dissipative atom-cavity system

We discuss the emergence of non-stationarity in open quantum many-body systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent, time-periodic oscillations induced by noisy contact with an environment. We use the Loschmidt echo and local observables to indicate the presence of a finite sized dissipative time crystal. Starting from the closed Hubbard model we then provide examples of dissipation mechanisms that yield experimentally observable quantum periodic dynamics and allow analysis of the emergence of finite sized dissipative time crystals. For a disordered Hubbard model including two-particle loss and gain we find a dark Hamiltonian driving oscillations between GHZ states in the long-time limit. Finally, we discuss how the presented examples could be experimentally realized.

https://iopscience.iop.org/article/10.1088/1367-2630/ababc4/pdf

Non-stationarity and dissipative time crystals: spectral properties and finite-size effects

We develop a Bethe ansatz based approach to study dissipative systems experiencing loss. The method allows us to exactly calculate the spectra of interacting, many-body Liouvillians. We discuss how the dissipative Bethe ansatz opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.

https://iopscience.iop.org/article/10.1088/1367-2630/abd124/pdf

Bethe ansatz approach for dissipation: exact solutions of quantum many-body dynamics under loss

We propose and demonstrate a versatile technique to measure the lifetime of the one-phonon Fock state using two-color pump-probe Raman scattering and spectrally resolved, time-correlated photon counting Following pulsed laser excitation, the n=1 phonon Fock state is probabilistically prepared by projective measurement of a single Stokes photon The detection of an anti-Stokes photon generated by a second, time-delayed laser pulse probes the phonon population with subpicosecond time resolution We observe strongly nonclassical Stokes-anti-Stokes correlations, whose decay maps the single phonon dynamics Our scheme can be applied to any Raman-active vibrational mode It can be modified to measure the lifetime of n≥1 Fock states or the phonon quantum coherences through the preparation and detection of two-mode entangled vibrational states

Two-Color Pump-Probe Measurement of Photonic Quantum Correlations Mediated by a Single Phonon.

We investigate the behavior of two coupled nonlinear photonic cavities, in the presence of inhomogeneous coherent driving and local dissipations. By solving numerically the quantum master equation, either by diagonalizing the Liouvillian superoperator or by using the approximated truncated Wigner approach, we extrapolate the properties of the system in a thermodynamic limit of large photon occupation. When the mean-field Gross-Pitaevskii equation predicts a unique parametrically unstable steady-state solution, the open quantum many-body system presents highly nonclassical properties and its dynamics exhibits the long-lived Josephson-like oscillations typical of dissipative time crystals, as indicated by the presence of purely imaginary eigenvalues in the spectrum of the Liouvillian superoperator in the thermodynamic limit.

Dissipative time crystal in an asymmetric nonlinear photonic dimer

New experiments provide the first direct observation of a single quantum of vibrational energy---a phonon---at ambient conditions, relying on techniques that offer a new approach to study quantum vibrational effects in molecules and bulk materials.

https://link.aps.org/pdf/10.1103/PhysRevX.9.041007

Preparation and Decay of a Single Quantum of Vibration at Ambient Conditions

Photonic resonators that allow an electromagnetic field to be confined in an ultrasmall volume with a long decay time are crucial to a number of applications requiring enhanced nonlinear effects. For applications to integrated photonic devices on chip, compactness and optimized in-plane transmission become relevant figures of merit as well. Here we optimize an encapsulated $\mathrm{Si}/{\mathrm{Si}\mathrm{O}}_{2}$ photonic-crystal nanobeam cavity at telecom wavelengths by means of a global optimization procedure, where only the first few holes surrounding the cavity are varied to decrease its radiative losses. This strategy allows us to theoretically achieve intrinsic quality factors close to 10 million, sub-diffraction-limited mode volumes, and in-plane transmission above 65%, in a structure with a very small footprint of about $8\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$. We address and quantitatively assess the dependence of the main figures of merit on the nanobeam length and on fabrication disorder. Finally, we study a system of two optimized and laterally coupled nanobeam cavities with the goal of demonstrating an unconventional photon blockade at room temperature in a monolithic passive device. We estimate the single-photon nonlinearity of this device and discuss the relevant figures of merit, which lead to sub-Poissonian photon statistics of the transmitted signal. Our results hold promise for prospective experiments in low-power nonlinear and quantum photonics.

Monolithic Silicon-Based Nanobeam Cavities for Integrated Nonlinear and Quantum Photonics

A single quantum of excitation of a mechanical oscillator is a textbook example of the principles of quantum physics. Mechanical oscillators, despite their pervasive presence in nature and modern technology, do not generically exist in an excited Fock state. In the past few years, careful isolation of GHz-frequency nano-scale oscillators has allowed experimenters to prepare such states at milli-Kelvin temperatures. These developments illustrate the tension between the basic predictions of quantum mechanics that should apply to all mechanical oscillators existing even at ambient conditions, and the complex experiments in extreme conditions required to observe those predictions. We resolve the tension by creating a single Fock state of a vibration mode of a crystal at room temperature using a technique that can be applied to any Raman-active system. After exciting a bulk diamond with a femtosecond laser pulse and detecting a Stokes-shifted photon, the 40~THz Raman-active internal vibrational mode is prepared in the Fock state $|1>$ with $98.5\%$ probability. The vibrational state is read out by a subsequent pulse, which when subjected to a Hanbury-Brown-Twiss intensity correlation measurement reveals the sub-Poisson number statistics of the vibrational mode. By controlling the delay between the two pulses we are able to witness the decay of the vibrational Fock state over its $3.9$ ps lifetime at room temperature. Our technique is agnostic to specific selection rules, and should thus be applicable to any Raman-active medium, opening a new generic approach to the experimental study of quantum effects related to vibrational degrees of freedom in molecules and solid-state systems.

Kilian Seibold

Papers

Two-Color Pump-Probe Measurement of Photonic Quantum Correlations Mediated by a Single Phonon.

Dissipative time crystal in an asymmetric nonlinear photonic dimer

Preparation and Decay of a Single Quantum of Vibration at Ambient Conditions

Monolithic Silicon-Based Nanobeam Cavities for Integrated Nonlinear and Quantum Photonics

Preparation and decay of a single quantum of vibration at ambient conditions